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DNITED STATES OP AMERICA.

ME0HANI0AL Drawing,

PROJECTION DRAWING.

ISOMETRIC AND OBLIQUE DRAWING.

WORKING DRAWINGS.

A CONDENSED TEXT FOR CLASS ROO

WALTER K. PALMER, M. E.,(OHIO STATE UNIVERSITY)

Department of Drawing, Miller Manual Labor School,

cro^et, virginia.

Columbus, Ohio :

c h a s . b . p a l m e k,

i'uhlishek.

Ai^

Copyright, 1894, by

SALTER K. PALMER.

[A/^ rights reserved.\

CONTENTS,

PAGE.

Introduction ii

PROJECTION DRAWING.Principles of Projection. page.

General Discussion 13

Fundamental Ideas of Projection 13

Application to Drawing 14

Notation 17

General Principles 19

Points ig

Lines 19

Surfaces and Solids 19

Point of Sight 20

Orthographic Projection 20

Scenographic Projection—Perspective 20

Drawing.

Conventional Lines 21

Exercise 22

Projections of a Point 22

Plate I 22

Projections of Lines 22

Projections of Right Lines 23

Principles 23

Plate II 24

Revolution 25

Of a Point 25

Principles 25

Plate III 26

IV CONTEXTS.PAGE,

Of Lines 26

True Length 26

Angles with H and V 26

Plate IV • 27

Plate V 27

Projection and Revolution 27

Of Plane Figures 27

Plate VI 28

Plate VII 28

Of Solids 28

Plate VIII 28

Shade Lines 29

Conventional Direction of Light • 29

Definition of Shade Lines 29

Exercise 30

Projection 30

Of Pyramid Cylinder and Cone 30

Plate IX 30

Of Sphere and Ellipsoid 30

Plate X 30

Third Projection 30

Plate XI 31

ISOMETRIC AXD OBLIQUE.Isometric. page.

Definition 35

Isometric Projection 35

Isometric Drawing 36

Isometric Axes 36

Isometric Lines 37

Use of Co-ordinates 37

Example 11

Shade Lines 38

Direction of Light 39

Plate XII 39

Plate XIII : 39

CONTENTS. VOblique. page.

How Differing from Isometric 40

Shade Lines 40

Cabinet Perspective 40

Plate XIV 40

Plate XV 40

WORKINCx DRAWINGS.Working Drawings. page.

Defined 43

How Made 43

The Three Views 43

Sections 43

Cross Sectioning 44

General Rules 45

Shade Lines 45

Drawing to Scale 46

Dimensioning 46

Dimension Line 46

Center Line 47

Isometric and Oblique for Working Drawings 47

General Views and Details 48

Details 48

How Made 48

Indexing 49

Conclusion , 49

PREFilGE.

The followinf^" pag"es contain the substance of a pro-

gressive course, beg'inning" with the essential principles

of elementary Projection Drawing, and passing on as

rapidly as is consistent with thoroughness, through

Isometric and Oblique Drawing, to the making of

ivorkmg drawing's.

The work is simply outlined, briefly, for the conveni-

ence of teacher and students. Explanations and illus-

trations by the teacher will be needed, and the course

may be supplemented or modified by him, as the needs

of a particular class may seem to require.

The little book is meant to be simply a "teacher's

help,"—a text strictly. It is, however, not a text,

such as the usual text books on Mechanical Drawing.

It embodies a general method of instruction. The aim

is to assist the student in developing for himself the

essential fundamental principles, in a natural and pro-

gressive order, starting with the most elementary

ideas, and working along by easy steps from one fact

to another, until the whole subject is unfolded.

The principles are in most cases simply stated. Thestudent should thoroughly verify each in order, with

the assistance of the teacher when necessary. Explan-ations and illustrations are not given, for each state-

ment follows directly and easily from what has just

preceded it, and it is one of the chief benefits of the

work, to verify the statements given and make simple

sketches and models to illustrate them.

8 PREFACE.

By little helps in the way of hints and illustrations,

and by questioning- to recall facts already established,

any student may be led to develop for himself all the

essential principles of the subjects treated, in such a

way that he cannot well forget them. At the sametime he acquires the habit of working- from a know-ledg-e of principles,—of thinking- and reasoning-, andrelying- on what he knows.

The plates g-iven are chosen to illustrate the princi-

ples brought out. Coming as they do at the close of

each topic, after the principles have been established,

they bring those principles into use, and fix the methodof their application, thus preparing for the next step.

No drawings are shown, and as few figures as pos-

sible are used, as it is expected that the teacher will

supply what is needed to clear up individual difficul-

ties, and that he will develop the actual work of draw-

ing, in the class room, by little helps and suggestions.

It is left altogether with the teacher as to what shall

be drawn under the head of "Working Drawings."

It is well to draw from measurements taken directly

from objects, or from sketches taken from machine

details. Shop exercises in a technical school afford

good practice. Revising a set of badly made shop

drawings, is good training. The work should be

arranged as progressively as possible.

Considerable practice should be given in making the

general drawing-s of complete machines, and detailing

from them; also in detailing from drawings made by

others; after which a course in designing may properly

be given.

A scheme for tabulating and indexing the details,

should be arranged by the student when he makes a

general drawing of a machine, and this should be fol-

lowed by those who detail from his drawing.

PREFACE. 9

It will be necessar}^ for the teacher to supply muchrelating" to working* drawings, in the way of conven-

tional methods of doing* various thing's, such, for in-

stance, as representing" screw threads, drawing" hexago-

nal bolt heads, etc. Such things are best given to

students individually, as they are ready to make use

of them. There are many little "ways" that mustbe broug"ht out by the teacher, as the need for themoccurs. He will of course draw upon standard worksof reference, his own experience, and reliable examples

of practice. Students should be frequently referred

to books by g"ood authorities, and to shop drawing"s

from the drafting" rooms of leading" machine works,

manufacturing companies and railroad shops.

Great pains should be taken to have thorougfhly g-ood

drawing's made. Accuracy, neatness and correctness

should be insisted upon. With proper attention to de-

tails, really fine work can be obtained from average

students.

A standard size of plate is recommended, until the

working" drawings are reached. A small size of plate

is preferable, as working" on a small drawing* is found

to enforce accuracy. "Freedom" can be quickly ac-

quired when the student comes to a larg"e drawing*. If

too much " freedom " be allowed at first, accuracy will

never be acquired.

Only the very best paper should be used. A stand-

ard plate of Keuffel & Esser's "normal" paper,

6| X 8^ ", with a border line \ " from the edge all

around, has proved very satisfactory.

Working" drawings should be penciled upon ordinary

"detail paper," then traced upon g-ood tracing* cloth,

and blue prints made from the tracings, if time allows.

When the student is done, the exercises and plates,

10 PREFACE.

and the working drawings he has made, which should

be thoroughly good work, and can easily be, with

proper attention on the part of the teacher, make with

the text a complete work upon the subject. Thus the

student helps to make for himself a work of reference

for his permanent use, and while so doing becomesthoroughly grounded in the principles and practices of

the work.

The method is not only natural and systematic, but

trial in the class room proves that it arouses and main-

tains the interest of the student, and eventually pro-

duces the most satisfactory results in the way of know-ledge and skill acquired, and training in systematic

work and study.

It is assumed that the student is reasonably skillful

in the use of instruments before taking up this course,

and it should be preceded by a thoroughly good course

in Geometric Construction Drawing. A previous in-

troduction into Geometry is necessar3% as a knowledge

of the terms and definitions of Geometry is assumed.

W. K. P.

Crozet, Va., April, 1894.

MECHANICAL DRAWING.

INTRODUGTION.

1. Mechanical Drawing is the art of making- drawing's

capable of representing- mechanical and architectural

structures, and the parts composing- them, so clearly

and completely that skilled mechanics can make those

structures exactly as they are intended to be, without

any further directions than those contained in the

drawing-s themselves.

2. Such drawing-s made expressly for the workmenare called " Working Drawings."

3. Evidently, these drawing-s, to meet the require-

ments, must express easily and perfectly all facts in

reg-ard to the f>ositio)i^ form and magnitude of objects

represented.

4. In other words, they must be capable of express-

ing- the g'eometry of all mathematical fig-ures,—solid as

well as plane,—for Geometry is defined as "that branch

of mathematics which treats of position^ form andmag'nititdey

5. They must represent these solid figures i)i space^

yet the drawing's must all be in one plane—that of the

paper.

6. It is evident, that the art of Mechanical Drawing-

must have as its foundation an exact mathematical

science. This is the science of " Projections."

11

12 MECHANICAL DRAWING.

7. Drawing's made in accordance with the methods

of Projection Drawing-, meet all requirements com-

pletely.

RBVIBW QUESTIONS.

1. What is meant by Mechanical Drawing?2. What are "Working drawings?"

3. What are the requirements to be met by working drawings ?

4. What is the definition of Geometry ?

5. What is the distinction between an art and a science ?

6. Is Mechanical Drawing a science or an art ? Or is it both ?

7. What is the foundation of Mechanical Drawing ?

8. How are the requirements of Mechanical Drawing met ?

PROJEGTION DR:HWING.

PRINCIPLES OF proj:ection.

8. Projection Drawing is tbe science and art of produc-

ing- drawings which shall represent completely all facts

of position, form and mag^nitude of all geometrical

quantities in space.

9. The Methods employed in Projection Drawing-, are

those of " Orthographic Projection," which is the basis of the

science of Descriptive Geometry,

FUNDAMENTAI< IDEAS OF PROJECTION.

10. In Projection Drawing, all objects are repre-

sented by their -projections upon fixed planes of refer-

ence. Hence an understanding of the geometrical

meaning of the term ''projection " is essential.

11. From Geometry we have :" The projection of a

point upon a straight line is Va^foot of the perpendicular

dropped from the point upon the line."

Thus:

A \ Q

vlfi^yK. \ ,

13


Let AB be any straight line, and P any point not in

the line. Let Pp be perpendicular to AB. Then p is

the projection of P upon the line AB,12. Similarly :

" The projection of a point upon a plane

is the foot of a perpendicular from the point to the plane.

Thus :

K

P is a point in space, and Pp a perpendicular from Pupon the plane ABCD. p \^t\i^ projection, then, of Pupon the plane.

13. The projection of any line, or surface, or solid, may be

found by finding- the projections of all of its points.

For lines and surfaces are but successions of points,

and solids are bounded by surfaces.

APPLICATION OF PROj:eCTION TO DRAWING.

14. Now consider two mathematical planes of in-

definite extent, intersecting- each other at rig-ht ang-les,

fixed in position, one horizontal and the other vertical.

Let the following- fig-ure represent limited portions of

these two planes :

APPLICATION OF PROJECTION TO DRAWING. 15

f'to ur-e §.

Let the vertical plane be denoted by Fand the hori-

zontal plane by //, and their line of intersection by GL.15. Now imagine a point to be situated in space in

one of the ang-les of these two planes, as shown in

Fig-. 4 :

Ptourc ¥.

16 MECHANICAIv DRA\YING.

Let P be the point in space in the angle of the twoplanes.

Now froject P upon the horizontal plane, and then

on the vertical plane. Then f> is the projection of Pupon the horizontal plane, and f is the projection of Pupon the vertical plane.

Draw pm and ft'in perpendicular to GL, in the hori-

zontal and vertical planes respectively.

16. Now it can readily be seen that these -projec-

tions of P upon the two planes, fix the position of P in

space, exactly. For if f> and p' be known, P can be

found at once by erecting* perpendiculars, which will

intersect in the position of P.

17. By means, then, of their projections upon two

fixed planes^ points anywhere in space may be repre-

sented. If points can be thus represented, lines and

surfaces, and all objects, may be represented in the

same way.

18. Now, while by this means all g^eometrical

quantities can be completely represented in space, no

application can be made of this method until somemeans is provided for bringing everything into one

plane, which can be made to coincide with the surface

of a sheet of drawing paper.

19. From Fig. 4 it is easily seen that all the quan-

tities may be readily brought into one plane, and with-

out destroying any of the essential relations.

Imagine the vertical plane to revolve backwardabout its intersection, GL^ while the horizontal plane

remains fixed. Let it revolve downward until it coin-

cides with the horizontal plane, carrying its projection

of the point with it to a new position p '

.

20. Evidently all quantities will retain their samerelations, and we may now deal with the revolved po-

sitions of the point, and no longer consider the point.

NOTATION. 17

21. When the two planes have been made to coin-

cide, they, with the projections of the point, may be

broug-ht into the plane of the paper, and will appear as

shown in Fig". 5 :

G nt

The line of intersection GL, is placed horizontal on

the drawing", with the projections upon the vertical

plane above, and those upon the horizontal plane below

it.

NOTATION.

TERMS EMPLOYED.

22. For convenience and brevity the following terms

are used :

(1) The two fixed planes are called " t/ic planes ofprojection,'' or '* the co-ordinate planes,"" or " the

planes of reference.''''

(2j The vertical plane of projection is called simply""' the vertical pkoie,"" or commonly, " K."

(3) The other is called '' the horizontal plane,'' or

simply, *'//."

(4) The line of intersection of the two planes is called

'' the g-ro2ind line," or briefly, '' GL."


(5) The projection upon V {p\ Fig's. 4 and 5;, is

called " t/ie vertical projection,'" or simply ''the Vprojecti0)1.''

(6) The projection upon H (/, Fig's. 4 and 5), is

called ''the horizoiital projection,^' or " the H pro-

jection.''

(7) The perpendiculars dropped from a point in space

(^Pp and Pp\ Fig". 4), are known as projecting" lines.

On the actual drawing-, Fig*. 5, pm and p ' in are com-monl}^ called the projecting- lines, thoug-h the}^ are

reall}^ the projections of the projecting* lines.

LETTERING.

23. (1) Points in space are denoted b}^ a capital let-

ter, as P, Fig-. 4.

(2) Projections of points are lettered with the corre-

sponding- small letters.

(3) Vertical projections are alwa^^s primed.

(4) Horizontal projections are not.

(5) If a point in space be moved into several positions

in succession, the same letter is used for all of the po-

sitions. The successive positions of the V projection

are denoted b}^ the same letter that is used for the first,

marked with ^^ ^^^, ^^', and so on in order. The H pro-

jections are marked with the corresponding- sub-

scripts, o, 3, 4, &c.

For example, if a point A should move successively

to ^", ^4"\ A"^', &c., its V projections would be let-

tered cC-, a^\ a^^\ a^^\ &c., and its H projec-

tions a, a.2, ((i, ct \. &c.

(6) Projections of plane "fig-ures and all surfaces and

solids, are lettered b}' selecting* prominent points on

them, and lettering these according- to the system of

lettering- points in g'eneral.

GENERAIv PRINCIPLES. 19

(7) Projections of particular angles are marked bysmall dotted arcs, and lettered with the minor letters

of the Greek alphabet. But one letter is used to de-

note an ang-le. The \ " /", &c., and subscripts, are

used on letters marking- the projections of ang-les, just

as on letters denoting* projections of points.

GENE^RAI, PRINCIPLES.

POINTS.

24. By reference to Fig-. 4, the following- funda-

mental principles are established in reg-ard to the pro-

jections of points, on the actual drawing", where the

two planes coincide, as in Fig*. 5:

(1) The two projections of a point in space fall on a

straig-ht line, which is perpendicular to the g-round

line. The vertical projection is above, the horizontal

belozv GL.

(2) The distance of the vertical projection from the

g-round line, is equal to the distance of the point from

the horizontal plane in space.

(3) The distance of the horizontal projection from

the g-round line, is equal to the distance of the point

from the vertical plane in space.

LINES.

25. As lines are made up of successions of points,

any line may be represented by finding- the two projec-

tions of all its points. These projections of the points

constitute i\\.^ projections of tlie line.

SURFACES AND SOLIDS.

26. In general, the two projections of surfaces andsolids may also be conside^xd as made up of the proiec-

tions of all the points composing- them.


27. In the case of limited portions of surfaces, it is

sufficient to consider simply the projections of the lines

bounding them.

28. In the case of solids, the projections of the

bounding- surfaces only are necessary.

29. Definite principles governing- the projections of

lines, surfaces and solids, and special directions for

particular cases, will be given as occasions arise for

their use.

POINT OF SIGHT.

30. Consider the two projections of an object. It

IS evident that either projection is just what would be

seen by an observer looking at the object in a direction

perpendicular to the plane of projection, if the eye

were at an infinite distance from the plane, and en-

dowed with correspondingly infinite power.

31. The point of sight is thus assumed at an infinite

distance so that the lines of sight will coincide with

the projecting lines of the object.

32. The vertical projection may then be considered

as a side or front view of the object. And in the sameway, the horizontal projection may be considered the^' top view."

33. When the point of sight is assumed in this wayat an infinite distance, the method of representation is

known as OrthogTaphic Projection.

34. When the point is at any position within finite

distance, the method is known as Scenographic, and

the resulting projection is called the Perspective of the

object.

35. Perspective views "d^x^ perfect pictures., but are

not suitable for working drawings, as the dimensions

of objects are not given by them in their true relation.

DRAWING—CONVENTIONAIv LINES. 21

DRAWING.

CONVENTIONAIv LINES.

Ordinary Full Line.

36. The projections of lines in space, either g-iven

or required, are drawn with an ordinary " weig'ht " of'"''/ttll line.''

Auxiliary Line—Fine Full Line.

37. Projections of lines that are auxiliary,—that is

used simply as aids,—are drawn with full lines madeenoug"h liner than the ordinary " full lines " to be in

marked contrast with them.

Construction Line.

38. The two projections of all points are always

joined with a " dotted line,'' made up of short dashes,

—

best about (^ of an inch long- and j^ of an inch apart,

—

of the weig'ht of the "fine full line."

This is also used to indicate the paths of moving'

points, as in cases of revolution, where the projections

of points move from one position to another.

Invisible Line.

39. Projections of lines which are hidden from view

by intervening- surfaces, are drawn with the " i)ivisible

line," which is made up of dashes about g^ of an inch

long-, and ^i of an inch apart, and of the weig-ht of the

"fine fuUline."

Gronnd Li)ie.

40. The g-round line is drawn with a heav}^ full

line, about twice the weig-ht of the ordinar}^ full line.

ISOLATED POINTS.

41. Projections of isolated points are marked withsmall fine crosses, as in Fii**. 5.

22 MECHANICAIv DRAWING.

D^XERCISB.

42. Prepare a plate of specimens of the conventional

lines to be used. Adopt lines of the proper "weight"and kind, and mark each line with its name. Leavespace upon the plate for two or three additional lines,

which will be met with later.

Keep this plate for reference, and always make all

lines according- to it.

PROJECTIONS OF A POINT.

43. The two projections of any point in space mayhe readily constructed directly from the fundamentalprinciples in regard to projections of points—page 13.

Plate I.

Represent by their two projections the six points sit-

uated as follows :

(1) A point J" from Fand 1| " from //.

(2) A point in F, and 1 " from H.

(3) A point 1 " from F, and k " from //,

(4) A point h " from F, and l\ " from H.

(5) A point I" from F, and in H.

(6) A point I" from F, and | " from H,

Directions : Draw the ground line thro the plate

a little below the middle, stopping it at equal dis-

tances from the end border lines. Place the points

so that their projecting lines on the drawing will be

equal distances apart. Letter the projections correctly.

Remark : For a plate 6^ '' by 8 Vz " with % '^ border, the ground

line should be ^Yz'^ from the lower border, stopping Yz'^ from each

€nd border line.

PROJECTIONS OF I^INES.

44. In general the projections of any line, curved or

straight, may be found by projecting all of its points,

PROJECTIONS OF RIGHT LINES. 23

but ill reality all the points can never be projected.

45. In the case of a curved line, a number of points are

chosen, as near tog"ether as the accuracy of the work

may demand, and their two projections found. Thecorresponding- projections of these two points are then

joined by smooth curves, which are the projections of

the curve in space.

46. In the case of a straig^ht line, it is sufficient to

simply project any two of its points, and then join the

corresponding- projections of these points by straight

lines.

PROJECTIONS OF RIGHT LINES.

47. The following- principles in regard to the pro-

jections of right lines are of great importance. Theymay be easily verified by a consideration of the lines in

space, situated according to the assumptions made.

They should be illustrated by simple models.

PRINCIPEES.

(1) The projections of a line can never be longer

than the line itself.

(2) When a line is parallel to either co-ordinate plane,

its projection on that plane is equal to the actual length

of the line in space. Its projection on the other plane

is parallel to the ground line.

(3) If a line is parallel to both co-ordinate planes,

it is parallel to the ground line, and both of its projec-

tions are parallel to the ground line.

(4) If a line is perpendicular to either co-ordinat^^^*

plane, its projection on that plane is a straijj;Kl^^rine

perpendicular to the ground line."^

(5) If a line is oblique to one co-ordinate plane, but

is parallel to the other, the projection on the plane to

which it is parallel gives the true size of the angle


which the line in space makes with the plane to whichit is oblique.

Evidently, from the preceding, when a line is oblique lo both planes^

neither projection gives its true lengtJi, or the angle it makes with either

plane.

(6) If a point be in a line, or a line is to pass throug*h

a g-iven point, the projections of the point must be on

the projections of the line.

(7) If two planes in space intersect, their projections

intersect, and the two projections of the point of inter-

section lie on a strai§"ht line, perpendicular to the

gfround line.

For the point of intersection is in both lines, hence its projections are

on the projections of both, and therefore at their intersection. Thepoint of intersection is simply a point, hence its projections are governed

by the laws of points in general.

(8) If two lines are parallel in space, their corre-

sponding- projections are parallel.

Principles (6) and (7) are equally true for lines in general, as well as

for straight lines.

Plate II.

Construct the two projections of each of the three

straig"ht lines situated as follows :

(1) A line, CK, 1| '' in length, parallel to F, and

parallel to H, 1| " above H, and \\" in front of T.

(2) A line BH, 2" in length, parallel to H and in-

clined to Fat an angle of 45°, the line to be Ig '' above

H, and the extremity nearest F, h " from F.

(3) A line FL, If " in length, parallel to F, and in-

clined at an angle of 30° to H, \ " in front of F, and its

lower extremity 1 " above H.Directions : Draw GL as before. Arrange the

drawing to suit the plate.

For standard 6|4f by 8>^ plates, the directions are : Place thefirst pro-

jecting line y^^^ from the left border. Leave Yz^^ between the projecting

lines of{i) and {2), and of {2) and ( j).

REVOLUTION OF A POINT. 25

RBVOI/UTION.

48. It often becomes necessary to revolve points,

and lines, and even entire fig-ures, in space, by means

of their projections. Evidently, any object may be re-

volved, if the principles g-overning" the revolution of a

^oint are known.

REVOLUTION OF A POINT.

49. A point is said to be revolved about a straight

line, as an axis, when it is so moved that it describes

the arc of a circle, whose center is the axis, and whose

plane is perpendicular to the axis.

50. The angle through which the point is revolved,

is measured by the arc described.

51. It is evident, that when all points of a figure

are revolved about an axis, and through the same

angle, their relative positions remain unchanged.

PRINCIPLES.

52. The following are true in regard to the revolu-

tion of points. They are readily verified by consider-

ing the quantities in space :

(1) If a point be revolved about an axis, perpendicu-

lar to one plane of projection, its projection on that

plane describes a circle arc. Its projection on the other

plane moves in a straight line parallel to the ground

line.

(2) If the axis be parallel to one plane of projection,

and oblique to the other, the projection of the point of

the plane to which the axis is parallel, moves in a

straight line perpendicular to the projection of the axis

on that plane. The other projection describes an

ellipse.

It is a general rule that when the axis is parallel to one plane, however

situated with respect to the other, that the projection of the point on the

plane to which the axis is parallel, moves in a straight line perpendicular

to the projection of the axis.


PivATE III.

I. Given the two projections of a point P, situated

\%" above H, and | " in front of F, and an axis perpen-

dicular to H, 1 " from the point, revolve the point about

the axis through an angle of 75°, and find its projec-

tions in the revolved position.

II. Given the point M in space, situated | " above

H, and \\ " from V. Revolve it, first about an axis

perpendicular to F, \\ " from it, through an angle of

90°, and then from this" position, about an axis perpen-

dicular to H, I " from it, revolve it through an angle of

60°, and construct its projections.

Directions : Draw GL as before. Arrange the

drawing to suit the plate. The axes being g-iven

quantities^ will be drawn with full lines. Letter all

the projections correctly. For the projections of the

radius of revolution in each case, use the "dotted

line " here.

REVOLUTION OF LINES.

53. When a straight line is oblique to both planes

of projection, neither projection shows its true length,

or the angle it makes with either plane.

54. To find the true length of a line so situated, or

the angles it makes with the planes of the projection, it

is necessary to revolve the line.

55. To revolve a straight line, it is only necessary to

revolve any two of its points through the same angle,

and join their revolved positions by a straight line.

Whenever possible, the axis of revolution is assumed

through some point of the line,—preferably one ex-

tremity. Then it is only necessary to revolve one

point,—usually, the other end.

REVOLUTION OF PLANE FIGURES. 27

Plate IV.

Given the two projections of a line, the left-hand end

of which is IJ " above H, and | " in front of F, and the

rig*ht-hand end \ " above H, and 1| " in front of F, its

H projection being* inclined 45° to GL.Find the true length of the line, and the angles it

makes with Fand with H,Directions: Draw GL as before. Arrange the

drawing in the middle of the plate.

The assumed, •and derived projections, are g'iven and

required, hence are drawn with the ordinary full line.

The lettering must show the order of the steps taken.

The projections of the axes of revolution, will not

be drawn. They will be omitted hereafter. But they

should be sketched for the study of problems.

The ground line may be left unlettered hereafter.

Plate V.

Find the two projections of a line 1| '' long, situated

so that its* left-hand end is | " above H, and 1^ " in

front of F, and its right-hand end is If " above H, and

1| " in front of F.

Directions: Draw 6^Z as usual. Place the problemin the middle of the plate.

Suggestion : It will be necessary to place the line first in an auxiliary

position,

REVOLUTION OF PLANE FIGURES.

56. In the case of polygons, it is only necessary to re-

volve their vertices, according to the principles of revo-

lution of points in general. All points of a polygon

must be revolved through the same angle.

57. In the case of a plane curve, points must be as-

sumed upon the curve as near together as the accuracyof the work demands, and these revolved, all thro the

same angle, according to the rules for points in general.


Plate VI.

Having' g-iven the two projections of a regular hex-

agon, in space, parallel to V, two sides of the hexagonparallel to //, about an axis perpendicular to //", thro

the left-hand extremity of the horizontal diameter, re-

volve the hexagon thro an angle of 45°, and construct

its projections.

Then revolve it again about the same axis, till the

plane of the figure inclines 60° to V. Revolve again»

till the hexagon comes perpendicular id V.

Directions: Draw (9Z as before. Let the diameter

of the circumscribing circle of the hexagon be 2 "

,

Letter the projections of the vertices of the hexagonin all their positions.

Plate VII.

Having- given a circle 2 " in diameter, in space, paral-

lel to H, about an axis perpendicular to F, tangent to

the circle, revolve it downward until its plane is in-

clined at an angle of 45° with H. Then assume an

axis thro the center of the circle, perpendicular to H^and revolve the circle about it through an angle of 30°.

Construct the projections in both positions.

Directions: Draw GL as usual. Arrange the

drawing to suit the plate.

PROJECTIONS OF SOLIDS.

58. The projections of solids may now be readily

constructed, from the principles of projection of lines

and surfaces.

Plate VIII.

I. Construct the two projections of a right regular

hexagonal prism, altitude 2\ ", radius of base | ",— the

base of the prism parallel to H, and two faces of the

prism parallel to V.

SHADE LINES. 29

II. Revolve the prism thro an ang"le of 30° to the

right, keeping- one point in the base at the same height

above H, and the two faces parallel to F.

Construct the projections in the revolved position.

Directions: Draw 6^Z whenever necessary to allow

space for the constructions.

Transfer the projections of the revolved position to

the right of those of the first, to avoid confusion.

SHAD^ LINES.

59. On drawings of solid objects, it is customary to

indicate by means of ''shade lines'' the surfaces on

which light falls, and on which no light falls.

CONVENTlONAIv DIRECTION OE EIGHT.

60. The light is assumed to come always from over

the left shoulder of the observer, in parallel straight

lines, in the direction of the body diagonal of a cube,

situated with two of its faces parallel to F, and twoparallel to H,

61. The projections, then, of a line, or " ray " of

light, both make angles of 45° with the ground line.

DEFINITION OE SHADE EINES.

62. The projections of all lines of an object, whichseparate light from dark surfaces, are shade lines.

63. They are drawn with heavy lines, of the weight

used for the ground line.

64. Shade lines, properly placed, add greatly to the

appearance of a drawing, and make it easier to under-

stand or " read."

65. The shade lines of a drawing are, in most cases,

easily determined by considering the direction of light,

and how the rays must strike upon the object repre-

sented. In some instances, however, it is difficult to


decide which should be shade lines, without a knowl-

edge of the methods of finding- the shadows of objects.

It is, however, rarely difficult in ordinary mechanical

drawing-, to determine the shade lines.

EXERCISE.

66. Place the proper shade lines on the projections

of Plate VIII.

Peate IX.

Construct the two projections of the following-

:

(1) A rig-ht regular hexagonal pyramid, base paral-

lel to H^ two edges of the base parallel to V,—radius

of base | '\ altitude of the pyramid 2\ "

.

(2) A right circular cylinder, axis perpendicular to

H, diameter 1^ ", altitude 2\ ".

(3) A right circular cone, axis perpendicular to H,

diameter of base 1\ " , altitude 2J "

.

Directions : Place all three objects the same height

above H^ and with their axes the same distance from

F.

Place the proper shade lines.

Plate X.

Construct the two projections of the following :

(1) A sphere 2 " in diameter, situated in space.

(2) A prolate ellipsoid of revolution, major axis

2J " , minor axis \\ ",

Directions : Arrange the drawing to suit the plate.

Decide in regard to shade lines.

Note. An ellipsoid of revolutio7i is generated by revolving an ellipse

about one of its axes. If about the major axis, a prolate ellipsoid is gen-

erated,—if about the minor axis, an oblate ellipsoid.

THIRD PROJECTION.

67. In certain special cases, the usual two projec-

tions do not completely represent an object. For in-

THIRD PROJECTION. 31

stance, if a cylinder should lie with its axis parallel to

the ground line, the H and V projections would not

represent it, as they would not then be different from

the two projections of a square ^rism similarly situated.

68. In every such case a third projection is neces-

sary. This is obtained as follows :

69. A plane is "passed" perpendicular to both Hand F, in any convenient position, just to the rig-ht of

the object to be represented.

70. This plane is indicated by the lines in which it

intersects ^ and V, These lines are called "traces,"

and are drawn with a line made up of a dash and three

dots repeated,—the dashes about 3_ " long-, and of the

weig"ht of the full line,—the dots like those of the con-

struction line,— which is the Descriptive Geometrysymbol for "Auxiliary Plane Trace."

71. This plane is known as the *' profile plane." Hav-ing- the third co-ordinate plane, the object is projected

upon it, and it is revolved to the right about its ver-

tical trace until it coincides with V. Then V is re-

volved down as usual, carrying- the projection of the

profile plane with it.

72. By means of these three projections, every pos-

sible geometric figure can be represented completely.

SHADE LINES.

73. Shade lines on the third projection are arbitra-

rily placed, just as they are in the vertical projection.

Plate XI.

Construct the projections of a hollow cylinder, out-

side diameter \\ ", inside diameter \" , length 2A ", sit-

uated with its axis parallel to H and to \\ | " in front

of F, and \\ " above H.Directions : Draw the ground line wherever neces-

sary. Arrange the drawing to suit the plate.


For the standard 6\^ " by SJ2 " plate, CL should be 2}^ " above the

lower border-

REVIEW QUESTIONS.

Q. S. What is Projection Drawing ?

Q. 9. Its methods are those of what scienee ?

Q. 10 Of what great branch of mathematics is Orthographic Projec-

tion the basis ?

Q. II. In Projection Drawing, how are objects represented ?

Q. 12. What is the "projection" of a point upon a line?

Q. 13. Urcr a rla-e? Illustrate.

Q. 14. E : " : ~ : - 1 ; r : r : : :- of a line found ?

O- 15. O:' a =ur:£Cc : O: a. solid?

O. 16. How may two projections of a point be made to £^x the posi-

tion of the point in sp a;e -

Q. 17. Howare:"::e : -_sr'. p'atirs a^su—e". :: ':e situated in space ?

Q. iS. If points are rxei : Litir : v: pre t::.:::-, ~ay 1 ne; :e also?

Q. 19. And surfaces, and so'.ii fr-res

-

Q. 20. Can any use be made of this r:e:'::: i ::' represeutatiru. with

the planes actually at right angles?

Q. 21. What is ueiei ary in order that application may be made of it?

Q. 22. H-vi~ li- rehire" eut met ^

Q- 23. Will the f^vj projections hx a point as well wheu the twc

planes are maie to cclncide?

Q. 24. How is the plane figure resulting from bringing the two planes

into coincidence, placed on the drawing? Make a sketch showing the

two projections of a point.

Q 25. What are the two fixed planes called ?

Q. 26. What is the name of the vertical plane ?

O. 27. Of the horizontal ?

Q. 28. Of the line of their intersection ?

Q, 29. What is meant by the //"projection of a point?

Q. 30. The J ' projection ?

Q. 31. What are projecting lines ?

Q. 32. How are the projections of a point lettered?

Q 33. How are the projections of the successive positions, P, P'\P"\ pi-^ Slc , of a point, lettered ?

Q. 34- How are the projections of plane figures lettered ?

Q. 35. Of solids ?

Q. 36. How are projections of imp>ortant angles marked?

Q. 37. How are the two projections of a point always situated with

respect to the ground line ?

Q. 38. How is the distance of a point from H shewn ?

O. 39. Which projection shows the distance of a point in space

from r?

REVIEW QUESTIONS. 33

Q. 40. How may the projections be considered as " views ?"

Q, 41. Which projection is the top view ?

Q. 42. What is the difference between orthographic and scenographic

projection ?

O. 43 What is the scenographic projection of an object commonlycalled ?

Q. 44. What are conventional lines ?

Q. 45. What are the ones used in Projection Drawing ?

Q. 46. How are the projections of curved lines found ?

Q. 47. Of straight lines ?

Q. 48. Can the project of a straight line be longer than the line itself ?

Q. 49. When will the projection equal the line ?

Q. 50. If a line is parallel to one plane and oblique to the other, whatis known regarding the projections ?

Q. 51. Which projection gives the angle with the plane to which it is

oblique ?

Q. 52. If a line is parallel to // and V, how are its projections

situated ?

Q. 53. If a line is perpendicular to one plane, what is its projection

on that plane ?

Q. 54. What is its other projection, and how situated ?

Q. 55. If a point be on a line, straight or curved, how are the projec-

tions of the point and line situated with respect to each other ?

Q. 56. If two lines, straight or curved, intersect, what is known of

their projections ?

Q. 57. If two straight lines are parallel in space, what is known of

their projection^ ?

Q. 58. When is a point said to be revolved about a straight line as an

axis ?

Q. 59. How must all points of a figure be revolved, not to change the

figure ?

Q. 60. If a point moves about an axis perpendicular to //, how does

its V projection move ?

Q. 61. What is the general statement of the principle ?

Q. 62. How does the projection of the point on the plane to which the

axis is parallel move, in all cases, whether the axis is perpendicular to

the other plane or not ?

Q. 63. Of what use are the principles of revolution ?

Q. 64. How is a straight line revolved ?

Q. 65. How is the true length of a line, oblique to both planes, found ?

Q. 66. If a line is inclined to both // and F, how is its angle with f/found ?

Q. 67. How would a polygon in space be revolved ?

Q. 68. Any curve ?

Q. 69. For what are shade lines used ?


Q. "o. What is the conventional direction of light ?

Q. 71. Are the rays of light assumed to be parallel ? Why ?

Q. 72. How are the projections of a ray of light inclined to the groundline ?

Q. 73. What lines are shade lines ?

Q. 74. How are they drawn ?

Q. 75. Of what use are shade lines ?

Q. 76. How are shade lines determined on a drawing ?

O. 77. Do two projections of all objects always represent themcomplete ?

Q. 78. What is a notable instance ?

Q. 79. What is done when the usual two projections are not sufficient ?

Q. 80. How is the third plane passed ?

Q. 81. When the projection has been formed on it, what is done with

it?

Q. 82. How is this third plane shown on the drawing ?

O. Ss. What is the kind of line used for the "traces ?"

Q. 84. What is the third plane called ?

Q. 85. Can everything be completely represented by three projections ?

Q. 86. How are shade lines placed on the third projection ?

ISOMETRIG :flND OBLIQUE DIMVIN6.

isom:etric.

DEFINITION.

74. Isometric Drawing is a method of representing" solid

objects so that their three principal dimensions will be

shown in their true values by means of but one view.

75. An isometric drawing- of an object is an approx-

imate -picture of it, which, unlike a true perspective

view, shows the leng*th, breadth and thickness in their

correct values.

ISOMETRIC PROJECTION.

76. Consider a cube in space, in the angle of the

two planes of projection, with its base parallel to the

horizontal plane, and one diag*onal of the base parallel

to the vertical plane.

77. Now let the cube be revolved forward from the

vertical plane, about an axis parallel to the g*round line

coinciding- with the diag-onal of the base, until a bodydiag-onal of the cube comes perpendicular to the vertical

plane.

78. It is readily seen now, that in this position the

vertical projection of the edg-es of the cube, which are,

of course, all equal in space, will be equal. For, all

the edg-es make equal ang-les with the diag-onal, or its

direction, which is perpendicular to \\ and hence equal

ang-les with V. Hence V projections are equal.

79. This F projection is the Isometric projection of the

cube.

3S


ISOMETRIC DRAWING.

80. In the isometric projection of a cube, the pro-

jections of the edg-es are all less, of course, than the

edg-es themselves in space ; but all the edges are

equally "foreshortened,"—that is, the projections are

prof)ortional to the edges themselves.

81. All the projection of the edges may, then, be

multiplied by a certain constant, and then will result a

drawing on which the lengths of the edges of the cube

are given exactly.

82. This drawing is called the " Isometric drawing " of

the cube, as distinguished from the Isometric projection.

83. To make an isometric drawing of a cube, the true

lengths of the edges are simply laid off in their proper

directions on the drawing.

84. These directions are known from the consider-

ation that the projections of the edges must form a

reg-itlar hexagon with its diagonals.

85. All lines, then, are either vertical or inclined to

the horizontal at angles of 30° either way.

86. Now, it is evident that not only cubes, but

all rectangular objects as well, may be represented byisometric drawings.

87. For, any rectangular object may be placed with

its edges parallel to those of the cube. Then they will

have the same directions on the drawing as those of

the cube, and will be equally " foreshortened," just as

are the edges of a cube.

88. These edges may be considered parallel in space

to three rectangular axes. These axes will have fixed

directions on all isometric drawings,—one vertical, one

inclined 30° one way, and the other 30° the other wa3^

89. They are called the isometric axes.

ISOMETRIC DRAWING. 37

90. All lines of an object: parallel to these axes, are

known as Isometric Lines.

91. All dimensions parallel to isometric lines, are

measured off their true length on the drawing-.

92. Measurements not parallel to isometric lines,

cannot be laid oif in their true values on the isometric

drawing*.

93. Isometric drawing is best adapted to representing- ob-

jects made up of plane surfaces, and whose principal

lines are parallel to the three rectang-ular axes.

94. In almost all other cases there is g-reat distortion

of the picture.

95. It is, however, sometimes necessary to repre-

sent non-isometric lines, and to draw curves isomet-

rically, and to represent special points on an isometric

drawing-.

USE OF CO-ORDINATES.

96. In all such cases it is necessary to have first

the orthog-raphic projections of the object. Prom these

the three rectang'uiar co-ordinates of any point of the

object may be found, referred to some point that can

be represented easily, and these then laid oif on the

drawing".

97. That is, the location of any -point may be deter-

mined by measurements along- isometric lines from

some point that can be shown isometrically.

EXAMPivE.

98. The use of co-ordinates in g-eneral is illustrated

by an example in Pig*. 6, which is a simple timber joint.

Evidently, the horizontal timber can be easily drawnin isometric, but the lines of the inclined piece and the

joint are non-isometric.


99. A single projection is sufficient here. From it.

Fig-. 6, get the " co-ordinates " Oa and ad of point Ij;

and Od and dc of any point C of the edge J^/I.

Construct the isometric drawing of the horizontal

piece OS. Then along OG on the drawing, la}^ off

Oa from O, and from a downward lay off ad. This

gives the lines I^d and bl^, as 7^ and 7? are on the iso-

metric line and can be laid off at once.

Next, to get the inclination of the other piece, lay off

Od from O along OG, and upward lay off dC. Thenthere are two points determined and J^H C3,n be drawn.

RK\^ parallel to FH on the object, hence will be on

the drawing.

The widths of the pieces are shown as usual. In

this way the complete isometric drawing is. readily

constructed.

100. By a similar use of co-ordinates obtained from

the ordinary projections, the isometric drawing of any-

thing may be constructed.

SHADE EINES.

101. Shade lines are placed in isometric drawings

ISOMETRIC DRAWING. 39

according" to the same principles as in ordinary

projection.

DIRECTION OF LIGHT.

102. The conventional direction of lig-ht is as be-

fore, from over the left shoulder, in the direction of

the body diag-onal of a cube. But here, this diag-onal

is inclined downward and to the rig-ht at an angle of

30° with the horizontal.

103. Hence the direction of light on an isometric draw-ing-, is 30° downward to the right.

PeatE XII.

Represent by isometric drawing,

(1) A cube with edges 1^ "

.

(2) An H shaped object formed from a cube 1| ''oe©''^^^

square, by cutting channels into twô opposite i::ftLl0feôf

the cube, and square m section.

Directions : Arrange in the middle of the plate.

Place the shade lines properly.^

Peate XIII.

Construct an isometric drawing of the model of a

timber joint, shown in Pig 6, using these dimensions :

Let OG=S".OM=l".

Width, 0W=\",0F= \\ ".

FH=Z\".HK=. OM^ I ".

Fd ^

bFIIÂ right angle.

Direclions: Place the drawing to suit the plate.

Show the proper shade lines.


OBlvIQU^ DRAWING.

104. Oblique Drawingf is very similar to Isometric.

The only difference is that in oblique drawing- one of

the axes, which in isometric is inclined at SO'', is madeJiorizontal, and all lines parallel to it.

105. The lines that are inclined, may make anyangfle with the horizontal, as well as 30°, and may in-

cline to the left or to the rig-ht. 30° and 45° are com-monly used, preferably 45°.

SHADE IvINES.

106. Shade lines are determined as in Isometric

Drawing-. When the inclined lines are to the rig-ht,

the shaded lines are situated on an object just as on

the isometric drawing- of it. But when the lines incline

to the left, they will be different, for the lig-ht mustcome in such a way as to make the front face illumi-

nated ; that is, the lig-ht cannot come from the rear,

hence all the illuminated faces of a cube or prism, or

other rectang-ular object, will be visible.

CABINET PERSPECTIVE.

107. Cabinet Perspective is a common term for Oblique

Drawing-. In this, the inclined lines are drawn at an

ang-le of 45° to the right.

PI.ATE XIV.

Represent in Oblique Drawing-,

(1) A cube \\ " square, making- the inclined lines on

the drawing- 30° to the rig-ht.

(2) The same cube, making- the inclined lines 60° t3

the rig-ht.

Directions : Place the shade lines properly.

Peate XV.

Represent in Oblique Drawing-,

REVIEW QUESTIONS. 41

(1) A cube 11 " square, making* the inclined lines

45° to the left.

(2) A cube 11 " square, making- the inclined lines

45° to the rig-ht.

Directions : Place the shade lines properly.

Compare the four drawing's of this cube in Plates

XIV and XV, and decide which represents the cube

best.

EXERCISE.

Represent in Cabinet Perspective the timber joint of

Plate XIII, using- the dimensions there g-iven.

REVIEW QUESTIONS.

Q. 87. What is Isometric Drawing ?

Q. 88. How does an isometric drawing differ from a perspective

view ?

Q. 89. How is the isometric projection of a cube obtained ? Illustrate.

Q 90. Why is it that the projections of the edges are all equal ?

Q. 91. What kind of a figure is then formed by them ?

Q. 92. How is the isometric drawing derived from the isometric

projection ?

Q. 93. Why is it allowable to multiply all the edges by the samething ?

Q. 94. How is an isometric drawing of a cube actually made ?

Q. 95. What directions have the edges on the drawing ?

Q. 96. How is it known ?

Q. 97. Can isometric drawings be made of anything but cubes ?

Q. 98. Why ? How ?

Q 99. What are the isometric axes ?

Q. 100. What are the isometric lines ?

Q. loi. What dimensions may be measured off on an isometric

drawing ?

Q, 102. Why cannot others ?

Q. 103. For what are isometric drawings best adapted ?

Q. 104. How are isometric drawings of curves and non-isometric lines

in general, drawn ? Explain and illustrate.

Q. 105. How are shade lines determined in isometric drawing ?

Q. 106. What is the conventional direction of light ?

Q. 107. What is the direction of a ray on the drawing ?

Q. 108. How does Oblique Drawing differ from Isometric.


O. 109. What are the usual directions for the axes in Oblique

Drawing ?

O. no. How are shade lines determined in Oblique drawing ?

Q. III. Do the shade lines of a cube come on the same edges when it

is shown with the inclined lines to the left, as when they are to the right ?

Q. 112. Why is this so ?

Q. 113. What is Cabinet Perspective ?

Q 114. Why so called ?

Ans. Because it is an approximation to true perspective, and was in-

tended to be especially useful to cabinet makers.

Q. 115. What are the directions of the principal lines in Cabinet

Perspective ?

WORKING DIMWINGS.

108. The object of a working drawing is, briefly, to showthe workman what to make and hozu to make it.

109. Working" drawings are made in accordance

with the principles of projection, but the rig-id laws,

and the refinements and conventionalities of Projection

Drawing, are not strictly observed. They are made in

the simplest and best way to accomplish the object for

which they were intended.

THE THREE VIEWS.

110. Usually the ordinary three projections are

employed, situated in their customary relation to each

other.

111. The vertical projection is called simply the

elevation, or the "front" or '*side view."

112. The horizontal projection is called the Plan, or*' top view."

113. The third projection is called the second elevation,

or "end elevation," or simply "end view,"—in somecases, "side view."

114. In some cases two end views are needed. Theview from the left is drawn to the right of the eleva-

tion, and the view from the right to the left of it.

115. When the views are not placed in their usual

relation, they must each be plainly marked.

SECTIONS.

116. In very many cases a better idea can be given

the workman of the shape and dimensions of an object,

43


if it is cut thro in some way by a plane, and the cut

surface drawn. Such drawings are called "sectional

views," or "sections."

117. Sections are used to show interiors of hollow

objects, and in all cases where the clearness of the

drawing will be increased.

118. Sectional views are arranged in convenient relation

to the other views. The best way of taking sections

and arranging the views, varies with each particular

case, and can best be learned by practice.

119. In many cases, pieces are better sectioned half

way thro, and the other half left as a simple view.

120. In very many other cases, it is sufficient to pass

a cutting plane only a little way, and then break out a

piece to disclose some special feature.

121. As a rule, cutting planes are passed parallel to

the planes of projection whenever possible.

CROSS SECTIONING.

122. In every sectional view, %vherever material is

cut, the cut surface is'

' sectioned'

' with fine lines

spaced equal distances apart, inclined 45° to the hori-

:Eontal.

123. The spacing will vary with the size of the draw-ing, being finer for small drawings than for large ones.

124. Cut pieces adjoining on the drawing, should

be sectioned in opposite ways. When it is impossible

to avoid sectioning two adjacent pieces in the samedirection, the ruling should offset. And the smaller

piece may be sectioned finer than the other. Thusthere is never any cause for confusion.

Note : Some favor the use of 30° and 60° lines for sectioning, whenthere are several cut surfaces adjacent. This is not necessary, however,

and is not so good.

125. Formerly there was a particular kind of cross

sectioning employed for every different kind of material.

GENERAlv RULES. 45

It is usual now, and much better, to mark each piece

by means of reference letters, or in words, to show the

kind of material to be used. This can be done for

pieces not sectioned, as well as for those that are.

There is no chance then for mistakes due to ig'nor-

ance of the conventionalities on the part of the

workmen.

126. No set of fixed rules can be laid down for

making" working" drawings, but a few g'eneral directions

should be observed.

127. The views to be shown, of an object, the man-ner of arranging- them, and the character and finish of

the drawing, are all largely matters of judgment on

the part of the draftsman in each instance. He mustbe guided by the purpose for which the drawing is in-

tended, and by the best practice.

128. On working drawings, "ground line" is

generally omitted. It is well to use it in drawings of

small pieces.

129. The "projecting lines," also, are never used

except on drawings of small pieces, and in cases wherethe use of a few of them will add to the clearness of

the drawing.

130. Drawings are lettered only when necessary for

reference, and then simply in whatever way may seembest in the particular case.

SHADB I^INISS.

131. Shade lines should always be placed on work-ing drawings according to the rules of Projection

Drawing. Shade lines correctly placed, add greatl3%

not only to the appearance of a drawing, but also to

the ease with which it may be used.


132. Shade lines are determined for sectional views

in the same way as for other views.

DRAWING TO SCAI<B.

133. All drawings should be "made to scale," so

that the dimensions on the drawing will bear a fixed

ratio to those on the object represented.

134. The best scale to adopt, is a matter of judg-

ment in each particular case, and depends on the size

of the drawing desired, and the peculiarities of the

thing represented. The scale should be chosen so that

the drawing will not be unnecessarih^ large, and yet

large enough to show the details of the thing repre-

sented, clearh'. The scale adopted should be noted on

the drawing, as, IJ "= 1'.

DIMENSIONING DRAWINGS.

135. Altho drawings are made to scale, all important

dimensions must be clearlv marked on the drawinsf in

figures. It is verv important that the figures be per-

fectly distinct. Feet are indicated by the prime mark

(0, and inches by the seconds '").

136. Dimensions that are horizontal, or nearly so,

read, of course, from left to right. Dimensions that

are vertical, must read from bottom to top.

137. The exact point, or lines, between which the

figures Sfive the measurements, are indicated bv a line

called the "dimension line," drawn between them.

138. The following is used as the dimension line,

—, a neat "arrowhead" being placed at

each end, the line being broken out for the figures.

The length of the dashes used, varies somewhat with

the size of the drawing and the use to be made of it.

139. The placing of the dimensions on a drawing,

is a matter requiring considerable attention. Every

CENTER IvINES. 47

necessary measurement must be gîven, but gîven only

once.

The "over all" dimension should always be given

^

and in close relation to those of the parts.

Care must be taken not to confuse a drawing- with

the fig"ures or the dimension lines.

CENTER IvINE.

140. It is often necessary to use a "center line.'^

Its uses will be learned by practice, as necessity for it

occurs. It would be drawn, for instance, in the draw-ing* of a shaft and pulleys, thro the center of the shaft.

In the plan of an engine, it would be drawn thro the

center of the shaft and also thro the center of the

cylinder, perpendicular to the shaft.

141. The line used is like the dimension line, but

made up of a dash and tvjo dots repeated.

142. The center line is also used to indicate the

location of a section. It is drawn where the cutting

plane is imagined to be passed.

ISOMETRIC AND OBIÎQUB FOR WORKINGDRAWINGS.

143. Isometric and oblique drawings are not customarily

used for working drawings. They may be used, how-ever, for simple things. They are well suited for

working drawings of simple rectangular objects,

but are not generally used. Their principal use

is for purposes of illustration. They serve to makedoubly clear anything that may be difficult to under-

stand from the ordinary working drawing. The}^ are

helpful to those who are not very ready in reading-

regular working drawings. In such cases, they ac-


company the reg"ular working* drawing's, and are not

dimensioned.

GENBRAI, VIEWS AND Dl^TAIIv DRAWINGS.

144. A drawing- showing- all the parts of a machineor other structure, put tog-ether in their proper places,

is called the "g-eneral drawing-," or "g-eneral view."

145. When a machine is being- desig-ned, g-eneral

views are made, usually plan, elevation, and second

elevation, and sometimes sections. These show all the

pieces in their proper relations to each other, drawn to

scale, so that the desig-ner is able to adapt them to each

other, and decide upon their dimensions.

DETAILS.

146. These g-eneral drawing's are usually too muchcrowded and confused to allow the dimensions of all

the pieces to be placed on them, so that the mechanic

can work from them.

147. Each piece must be picked out from the g-eneral

drawing-, and a separate and larg-er drawing- made of

it to scale, with the dimensions all fig-ured. These draw-

ing-s of the pieces are called *' Detail Drawings," or

*' Details."

148. In cases where much machine work is to be

done on the pieces, a set of details is made for the pat-

tern maker, and another set, showing- the dimensions of

the finished pieces and the machine work required, is

made for the machinist. The instructions to both the

pattern maker and the machinist, may often be shownon one drawing-.

149. Detail drawings are made in pencil on ordinary

paper, preferably "detail paper," and then tracing-s

made, which may be preserved. Prints are made for

the workmen.

GENERAL VIEWS AND DETAIL DRAWINGS. 49

INDEXING.

150. Details of complicated machines must be plainly

marked, and numbered and indexed according- to some

system, so that the tracing* of any detail may be readily

found.

151. Further knowledg^e of the endless variety of

methods followed by draug^htsmen in making* working*

drawings can only be acquired by prolong*ed practice

under the direction of some one competent to instruct.

In time, the ^'' idea'" of it all will become so instilled

into one that he can work out ways for himself to fit

any case he may be called upon to handle.

RBVI:EW QTJiESTIONS.

Q. ii6. What is the object of working drawings ?

Q. 117. How are working drawings made ?

Q. 118. Are any rigid set of rules followed strictly ?

Q. 119. What is to guide then, in making a working drawing for aparticular purpose ?

Q. 120. What is the common name for the vertical projection ?

Q. 121. For the horizontal projection ?

Q. 122. When two end views are needed, how are they placed ?

Q. 123. Is it allowable to place the views in any other relation ?

Ans. Yes, if desirable for any special reason. Each view may be on a

separate sheet, if necessary. (See Sec. 115.)

Q. 124. What are sections ?

Q. 125. For what are they used ?

Q. 126. How should the cutting plane be passed ?

Q. 127. Can any fixed rules be given for taking sections ?

Q. 128. What is to guide, then ?

Q. 129. How are cut surfaces shown on a drawing ?

Q. 130. How is cross sectioning done ?

Q. 131. Are there any fixe' rules that can be laid down for makingworking drawings, to cover all cases ?

Q. 132. Why ?

Q- 133- What are some general rules that should be observed ?

Q. 134. Are shade lines used on working drawings ?

Q. 135. How are the shade lines determined for sections ?

Q. 136. What governs the choice of the best scale for a drawing ?

Q. 137. What are some rules to be observed in dimensioning drawings?


What is the conventional dimension line ?

For what purposes is a center line used ?

What is the conventional center line ?

Are isometric and oblique drawings used as working drawings ?

Are they suitable for working drawings ?

How are they generally used, when at all ?

What is meant by a general view ?

When is such a drawing required ?

What are detail drawings ?

How are detail drawings usually prepared ?

How can it be arranged so that the shop drawing of any par-

ticular detail of a large complicated machine may be readily found ?

Q. 149. What may be said of acquiring familiarity with the many lit-

tle "ways" of practical draughtsmen ?

Q 138.

Q 139-

Q- 140.

Q. 141.

Q. 142.

Q. 143.

Q- 144.

Q 145.

Q- 146.

Q. 147.

Q 148.

ERRATA.1. Page 22, Section 43 : The reference should be to page 19, instead

of 13.

2. Page 23 : Sub-section [4) should read as follows :

*'(4) If a line is perpendicular to either co-ordinate plane, its projec-

tion on that plane is a point, and its projection on the other plane is a

straight line perpendicular to the ground line."

3. Page 24, sub-section (7) : For " two planes in space, " read "twolines in space.

"

4. Page 25, section 49 : Vox " whose center is the axis," read

" whose center is in the axis."

5. Page 29, Directions : For " whenever," read " wherever."

project," read " projection,"

moves," read ** revolves."

For " Complete," read " completely."

9. Page 35, section 78 : The last sentence should read, " Hence

their V projections are all equal."

10. Page 36, section 81 : In the first line, for " projection," read'' projections." In the second line, for " then," read " there."

1 1

.

Page 38, section 99 : For dc read dC.

12. Page 39 : Problem (2), under Plate XII, should read as follows :

"(2) An H~shaped object formed from a cube i^ ^' square, b)- cut-

ting channels into two opposite faces of the cube, the channels to be

one-third of the width of the cube, and square in section."

13. Page 40, section 106: For "shaded lines," read "shade lines."

14. Page 41, O. 100: Omit "the."

15. Page 45, section 128 : Insert "the" before " ground line."

16. Page 45 : The last word on the page should be "read," instead

of "used."

6. Page 33, Q. 48: P'or

7. Page 33, 0. 60: For

8. Page 34, Q. 77: For

-^^

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